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\(2.3^x=10.3^{12}+8.27^4\)
=>\(2.3^x=10.3^{12}+8.\left(3^3\right)^4\)
=>\(2.3^x=10.3^{12}+8.3^{12}\)
=>\(2.3^x=3^{12}.\left(10+8\right)\)
=>\(2.3^x=3^{12}.18\)
=>\(2.3^x=3^{12}.3^2.2\)
=>\(2.3^x=3^{14}.2\)
=>\(3^x=3^{14}\)
=>x=14
\(\Rightarrow2.x^3=9565938\)
\(\Rightarrow x^3=9565938:2=4782969\)
\(\Rightarrow x=168.49....\)
\(a,2.3^x=10.3^{12}+8.27^4\)
\(\Leftrightarrow2.3^x=3^{12}\left(10+8\right)\)
\(\Leftrightarrow2.3^x=3^{12}.18\)
\(\Leftrightarrow2.3^x=3^{12}.3^2.2\)
\(\Leftrightarrow2.3^x=2.3^{14}\)
\(\Rightarrow3^x=3^{14}\)
\(\Rightarrow x=14\)
\(b,2^{4x}.3^6=12^6\)
\(\Leftrightarrow2^{4x}.3^6=2^{12}.3^6\)
\(\Rightarrow2^{4x}=2^{12}\)
\(\Rightarrow4x=12\)
\(\Rightarrow x=3\)
a/ 2710 : 9x - 1 = 320 => 330 : 9x - 1 = 320 => 9x - 1 = 330 : 320
=> 9x - 1 = 310 => 9x - 1 = 95 => x - 1 = 5 => x = 6
b/ 3x + 3x - 2 = 90 => 3x + 3x . 3-2 = 90 => 3x . (1 + 3-2) = 90
=> 3x . \(\frac{10}{9}\)= 90 => 3x = 81 => 3x = 34 => x = 4
B1:
Ta có: \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}-2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}-2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1-5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}\)
\(=\frac{2.\left(-4\right)}{3.5}=-\frac{8}{15}\)
B2:
Ta có: \(1+3+5+...+x=1600\)
\(\Leftrightarrow\frac{\left(x+1\right)\cdot\left(\frac{x-1}{2}+1\right)}{2}=1600\)
\(\Leftrightarrow\left(x+1\right)\cdot\frac{x+1}{2}=3200\)
\(\Leftrightarrow\left(x+1\right)^2=6400\)
Xét theo dãy tăng tiến ta thấy được giá trị của x càng tăng
=> x dương => x + 1 dương
\(\Rightarrow x+1=80\)
\(\Rightarrow x=79\)
3\(^x\) . 3 = 43
=> 3\(^{\left(x+1\right)}\) = 43
=> Không có giá trị x thoả mãn .
49 . \(7^x\) = 2041
7\(^2\) . 7\(^x\) = 2041
7\(^{\left(x+2\right)}\) = 2041
=> \(7^{\left(x+2\right)}\) = 7\(^4\)
=> x + 2 = 4
=> x = 2
2.3x = 10.312 + 8.274
2.3x = 10.312 + 8.312
2.3x = 312.(10 + 8)
2.3x = 312.18
2.3x = 314.2
Vậy x = 14
\(2.x^3=10.3^{12}+27^4.8\)
\(2.x^3=2.5.3^{12}+3^{12}.2^3\)
\(2.x^3=2.3^{12}.\left(5+4\right)\)
\(x^3=3^{12}.9\)
\(x^3=3^{14}\)
2. x\(^3\)= 10. 3\(^{12}\)+ 27\(^4\). 8.
2. x\(^3\)= 10. 3\(^{12}\)+ 3\(^{3^4}\). 8.
2. x\(^3\)= 10. 3\(^{12}\)+ 3\(^{12}\). 8.
2. x\(^3\)= 3\(^{12}\)( 10+ 8).
2. x\(^3\)= 3\(^{12}\). 18.
2. x\(^3\)= 531441x 18.
2. x\(^3\)= 9565938.
x\(^3\)= 9565938: 2.
x\(^3\)= 4782969.
Vậy x\(^3\)= 4782969.
Bài này đã giải rồi nha, e coi lại câu hỏi trước nha